How old is the Monitor and is it working properly? I have a 19" LG monitor that started to do the exact same thing it would power up and be fine one day but then a day or two later it would be blank even though the little blue light would be on showing that the monitor had power.
I had thought that it was my Video card but after going through two other video cards and then different DVI cords from the cards to the monitor I ended up digging up and old 17 " and plugged that in and never had a problem since.
SO I would check the simple things first then go from there.